# Velocity

The average speed of an object is defined as the distance traveled divided by the time elapsed. The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

Velocity is a vector quantity, and average velocity can be defined as the displacement divided by the time. The units for velocity can be implied from the definition to be meters/second or in general any distance unit over any time unit. For the special case of straight-line motion in the x direction, the average velocity takes the form:

$v_{avg}=\overline{v}=\dfrac{x_2-x_1}{t_2-t_1}$

You can approach an expression for the instantaneous velocity at any point on the path by taking the limit as the time interval gets smaller and smaller. Such a limiting process is called a derivative and the instantaneous velocity can be defined as:

$v_{inst}=\lim_{\Delta t\rightarrow 0}\dfrac{\Delta x}{\Delta t}=\dfrac{dx}{dt}$

## Velocity measurement

The measurement of velocity can be carried out on all moving material bodies, whether they are solids, compressible or incompressible (liquids or gases); in particular, if this measurement is carried out on a gas in motion, it is necessary to distinguish the type and method of measurement depending on whether the gas is moving at a speed much lower than that of sound (the measurement is carried out as for liquids); or:

• speed much lower than that of sound (the measurement is carried out as for liquids);
• subsonic speed
• supersonic speed;
• transonic speed.

For solid moving material bodies, velocities are either angular or linear (or a combination of these), so the measurement of velocity in this case will involve the determination of mechanical power.

## Related keywords

• Speed measuring instruments